矩阵方程的自反和反自反矩阵解

矩阵方程 的自反和反自反矩阵解

关键词：自反矩阵;反自反矩阵;矩阵方程;Frobenius范数;矩阵最佳逼近问题

The reflexive and anti-reflexive solutions of the

matrix equation

Abstract :An complex matrix is said to be a generalized reflection matrix if and .An complex matrix ia said to be a reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrixs , if . An complex matrix ia said to be a reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrix , if .This paper establishes the necessary and sufficient conditions for the existence of and the expressions for the reflexive and anti-reflexive with respect to a generalized reflection matrixs solutions of the matrix equation .In addition, incorresponding solution set of the equation.The explicit expression of the nearest matrix to a given matrix in the Frobenius noum have been provided.

Keywords:Reflexive matrix; Anti-reflexive matrix; Matrix equation; Frobenius norm; Matrix nearness problem.